美赛标题英文和翻译

2013 Contest Problems

MCM PROBLEMS

PROBLEM A: The Ultimate Brownie Pan

When baking in a rectangular pan heat is concentrated in the 4 corners and the product gets overcooked at the corners (and to a lesser extent at the edges). In a round pan the heat is distributed evenly over the entire outer edge and the product is not overcooked at the edges. However, since most ovens are rectangular in shape using round pans is not efficient with respect to using the space in an oven.

Develop a model to show the distribution of heat across the outer edge of a pan for pans of different shapes - rectangular to circular and other shapes in between.

Assume

1. A width to length ratio of W/L for the oven which is rectangular in shape.

2. Each pan must have an area of A.

3. Initially two racks in the oven, evenly spaced.

Develop a model that can be used to select the best type of pan (shape) under the following conditions:

1. Maximize number of pans that can fit in the oven (N)

2. Maximize even distribution of heat (H) for the pan

3. Optimize a combination of conditions (1) and (2) where weights p and (1- p) are assigned to illustrate how the results vary with different values of W/L and p.

In addition to your MCM formatted solution, prepare a one to two page advertising sheet for the new Brownie Gourmet Magazine highlighting your design and results.

问题A：终极布朗尼潘

当在一个矩形的锅烘烤时热量会在4个角落集中，并使产品在拐角

处（以及在较小程度上在边缘处）加热过度。在一个圆形盘的热量

被均匀地分布在整个外缘并且在边缘处的产品不会加热过度。然而

，相对于使用的空间的烘箱中，由于大多数烤炉是矩形的形状使用圆形平底锅是效率不高。

开发一个模型来显示不同形状的平底锅锅的外边缘之间的热分布-矩形到圆形和在两者之间的其它形状。

假设

1。烘箱是矩形的形状，宽度长度比为W / L，定名为A；

2。在A中，每盘必须有一个区域。

3。最初两个烘烤架均匀地间隔开。

开发模型，使其在下列条件下可用于选择的最佳类型的盘（形状）：

1。锅数量最大情况并适合烤箱的锅形状（N）

2。使锅的热量最大化均匀分布（H）的锅形状

3。优化的组合的条件（1）和（2）式中的权重p和（1 - p）被分配的结果来说明，W / L 和 p的不同的值的变化。

在除了您的MCM格式化论文外，制备一到两页的广告单，发到布朗

尼美食杂志，注意突出您的设计和结果。

PROBLEM B: Water, Water, Everywhere

Fresh water is the limiting constraint for development in much of the world. Build a mathematical model for determining an effective, feasible, and cost-efficient water strategy for 2013 to meet the projected water needs of [pick one country from the list below] in 2025, and identify the best water strategy. In particular, your mathematical model must address storage and movement; de-salinization; and conservation. If possible, use your model to discuss the economic, physical, and environmental implications of your strategy. Provide a non-technical position paper to governmental leadership outlining your approach, its feasibility and costs, and why

it is the “best water strategy choice.”

Countries: United States, China, Russia, Egypt, or Saudi Arabia

问题B：水，水，无处不在